Conventionally, an air-fuel ratio controlling apparatus has been widely known, which is provided with a three-way catalyst disposed in an exhaust gas passage of an internal combustion engine, and an upstream air-fuel ratio sensor and a downstream air-fuel ratio sensor disposed upstream and downstream, respectively, of the three-way catalyst in the exhaust gas passage. This air-fuel ratio controlling apparatus calculates an air-fuel ratio feedback amount based on an output of the upstream air-fuel ratio sensor and an output of the downstream air-fuel ratio sensor, and performs a feedback control upon an air-fuel ratio (air-fuel ratio of the engine) of air-fuel mixtures supplied to the engine using the air-fuel ratio feedback amount, in such a manner that the air-fuel ratio of the engine coincides with a stoichiometric air-fuel ratio. Further, an air-fuel ratio controlling apparatus has been suggested, which calculates an air-fuel ratio feedback amount based on only one of the output of the upstream air-fuel ratio sensor and the output of the downstream air-fuel ratio sensor, and performs a feedback control upon the air-fuel ratio of the engine using the air-fuel ratio feedback amount. The air-fuel ratio feedback amount used in such air-fuel ratio controlling apparatuses is a control amount commonly used to all of the cylinders.
Incidentally, an electronically-controlled fuel injection type internal combustion engine is generally provided with at least one fuel injector in each of the cylinders or in each of intake ports each communicating with one of the cylinders. Therefore, when a characteristic (or property) of the fuel injector of a specific cylinder becomes a “characteristic that the specific injector injects a more excessive amount of fuel than an instructed fuel injection amount”, only the air-fuel ratio of an air-fuel mixture supplied to that specific cylinder (the air-fuel ratio of that specific cylinder) shifts to an extremely richer side. That is, a non-uniformity among air-fuel ratios of the cylinders (deviation in air-fuel ratio among the cylinders, an air-fuel ratio imbalance among the cylinders) becomes large. In other words, an imbalance is generated in the air-fuel ratios of individual cylinders.
In this case, the average of the air-fuel ratios of the air-fuel mixtures supplied to the entire engine becomes an air-fuel ratio richer than the stoichiometric air-fuel ratio. Therefore, the air-fuel ratio feedback amount commonly used for all the cylinders causes the air-fuel ratio of the above-mentioned specific cylinder to shift to a leaner side, so that the air-fuel ratio of the specific cylinder becomes closer to the stoichiometric air-fuel ratio, and simultaneously, causes the air-fuel ratios of the other cylinders to shift to a richer side, so that the air-fuel ratios of the other cylinders deviate from the stoichiometric air-fuel ratio. As a result, an average of the air-fuel ratios of the air-fuel mixtures supplied to the entire engine becomes approximately equal to the stoichiometric air-fuel ratio.
However, the air-fuel ratio of the above-mentioned specific cylinder is still in a richer side with respect to the stoichiometric air-fuel ratio, and the air-fuel ratios of the other cylinders are still in a leaner side with respect to the stoichiometric air-fuel ratio, so that the combustion state of the air-fuel mixture in each of the cylinders is different from its perfect (complete) combustion state. As a result, an amount of emissions (an amount of unburnt substances and an amount of nitrogen oxides) discharged from each of the cylinders increases. Therefore, even when the average of the air-fuel ratios of the air-fuel mixtures supplied to the engine coincides with the stoichiometric air-fuel ratio, the three-way catalyst cannot purify the increased emissions, so that there is a possibility that the missions become worse.
Therefore, it is important to detect that the non-uniformity among the air-fuel ratios of the cylinders becomes excessive (generation of an imbalance state in air-fuel ratio among the cylinders), since some measures can be taken in order not to worsen the emissions. Note that an imbalance state in air-fuel ratio among the cylinders is generated due to various factors such as a case where the characteristic of the fuel injector of the specific cylinder becomes a “characteristic that the injector injects an excessively small amount of fuel than the instructed fuel injection amount”, or a case where distribution of an EGR gas and an evaporated fuel gas to each of the cylinders becomes non-uniform.
One of such prior art apparatuses for determining whether or not the non-uniformity among air-fuel ratios of the cylinders has occurred is configured so as to obtain a locus (trajectory) length of the output (output signal) of an air-fuel ratio sensor (the above-mentioned upstream air-fuel ratio sensor) disposed at an exhaust gas aggregated portion where exhaust gases from the plurality of cylinders are aggregated, and to compare the locus length with a “reference value varying in accordance with an engine rotational speed and an intake air amount”, and to determine whether or not the imbalance state in the air-fuel ratios among the cylinders has occurred in accordance with the comparison result (for example, refer to U.S. Pat. No. 7,152,592). It should be noted that, in the present specification, the determination of whether or not an imbalance state in air-fuel ratios among cylinders has occurred is also simply referred to as an “air-fuel ratio imbalance among cylinders determination”, or an “imbalance determination”.